Formal privacy metrics provide compliance-oriented guarantees but often fail to quantify actual linkability in released datasets. We introduce CVPL (Cluster-Vector-Projection Linkage), a geometric framework for post-hoc assessment of linkage risk between original and protected tabular data. CVPL represents linkage analysis as an operator pipeline comprising blocking, vectorization, latent projection, and similarity evaluation, yielding continuous, scenario-dependent risk estimates rather than binary compliance verdicts. We formally define CVPL under an explicit threat model and introduce threshold-aware risk surfaces, R(lambda, tau), that capture the joint effects of protection strength and attacker strictness. We establish a progressive blocking strategy with monotonicity guarantees, enabling anytime risk estimation with valid lower bounds. We demonstrate that the classical Fellegi-Sunter linkage emerges as a special case of CVPL under restrictive assumptions, and that violations of these assumptions can lead to systematic over-linking bias. Empirical validation on 10,000 records across 19 protection configurations demonstrates that formal k-anonymity compliance may coexist with substantial empirical linkability, with a significant portion arising from non-quasi-identifier behavioral patterns. CVPL provides interpretable diagnostics identifying which features drive linkage feasibility, supporting privacy impact assessment, protection mechanism comparison, and utility-risk trade-off analysis.